Question

Solve the following problem :

The probability distribution of a discrete r.v. X is as follows.

X	1	2	3	4	5	6
(X = x)	k	2k	3k	4k	5k	6k

Determine the value of k.

Answer 1

Since P(X) is the probability distribution of X,

\[\sum\limits_{x =1}^{6}\text{P}(X = x) = 1\]

∴ k + 2k + 3k + 4k + 5k + 6k = 1
∴ 21k = 1

∴ k = `(1)/(21)`.